0 KB522 KB52 KB200820252011Sarti, Cristinaštevilka:2letnik:4str. 291-311COBISSID:16267865ISSN:1855-3966URN:URN:NBN:SI:doc-W7QB95FAenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneabipartite graphsdessins d'enfantsdifference setsdvodelni grafifinite geometriesFrobenius automorphismFrobeniusov automorfizemgraph embeddingskončne geometrijeRiemann surfacesRiemannove ploskveSinger groupsSingerjeve grupevložitve grafovWada dessinsWada dessins associated with finite projective spaces and Frobenius compatibility|Dessins d'enfants (hypermaps) are useful to describe algebraic properties of the Riemann surfaces they are embedded in. In general, it is not easy to describe algebraic properties of the surface of the embedding starting from the combinatorial properties of an embedded dessin. However, this task becomes easier if the dessin has a large automorphism group. In this paper we consider a special type of dessins, so-called Wada dessins. Their underlying graph illustrates the incidence structure of finite projective spaces ?$\Bbb P^m (\Bbb F_n)$?. Usually, the automorphism group of these dessins is a cyclic Singer group ?$\Sigma _\ell$? permuting transitively the vertices. However, in some cases, a second group of automorphisms ?$\Phi_f$? exists. It is a cyclic group generated by the Frobenius automorphism. We show under what conditions ?$\Phi_f$? is a group of automorphisms acting freely on the edges of the considered dessinsTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije